Well, there is only one way to know whether an Actor existed at a certain point in the past: if you receive a message from it. All of the above are just variations on this theme.
That said, once you have the ActorRef, you can use DeathWatch to be notified about that actor’s termination. But not yet having received the Terminated message does not mean that the actor is still alive: the Terminated might already be on its way.
Think of Actors as people who can only communicate by sending email. That analogy works quite well for the semantics of their interaction.